Bi-Directional Polarised Light Transport

Transcription

1 Bi-Directional Polarised Light Transport M. Mojzík T. Skřivan A. Wilkie J. Křivánek Charles University in Prague 1/37

2 Motivation 2/37 M. Mojzı k, T. Skr ivan, A. Wilkie & J. Kr iva nek Bi-Directional Polarised Light Transport

3 Motivation 3/37 M. Mojzı k, T. Skr ivan, A. Wilkie & J. Kr iva nek Bi-Directional Polarised Light Transport

4 State of Polarisation Support Goal: Support polarised light in bi-directional light transport algorithms 4/37

5 State of Polarisation Support Goal: Support polarised light in bi-directional light transport algorithms Previous implementations: only for uni-directional path-tracer details already gathered [Wilkie et al 2012] 4/37

6 State of Polarisation Support Goal: Support polarised light in bi-directional light transport algorithms Previous implementations: only for uni-directional path-tracer details already gathered [Wilkie et al 2012] Can we use it for bi-directional light transport? 4/37

7 Contribution 5/37

8 Contribution Radiometry of polarised light transport 5/37

9 Contribution Radiometry of polarised light transport Reference implementation of bi-directional algorithms 5/37

10 Proposed theory 6/37

11 Why New Theory? Goal: Generalize Rendering eq.: L o = L e + f(ω i, ω o )L i (ω i ) dωi S 2 Measurement eq.: I = W e (ω)l i (ω) dω S 2 7/37

12 Why New Theory? Goal: Generalize Rendering eq.: L o = L e + f(ω i, ω o )L i (ω i ) dωi S 2 Measurement eq.: I = W e (ω)l i (ω) dω S 2 What is radiance L, BSDF f and importance W in the context of polarised light? Radiance: classical: L : M S }{{} 2 R ray space polarised: L : M S 2? 7/37

13 Brief Overview of Polarised Light 8/37

14 Stokes Vector We describe polarised light with Stokes vector S S = (S 0, S 1, S 2, S 3 ) ( ) ( ) ( ) The Stokes vector depend on the choice of the coordinate system 9/37

15 Mueller Matrix Muller matrix M describes what happens to the light when it bounces of the surface S 0 M 11 M 12 M 13 M 14 S 0 S 1 S 2 = M 21 M 22 M 23 M 24 S 1 M 31 M 32 M 33 M 34 S 2 S 3 M 41 M 42 M 43 M 44 S 3 Its components depend on the coordinate frame of the incoming and outgoing light 10/37

16 Proposed Theory 11/37

17 Radiance Radiance in polarised light transport L : M S 2? 12/37

18 Radiance First guess: L : M S 2 R 4 12/37

19 Radiance First guess: Bad choice: L : M S 2 R 4 missing coordinate frame 12/37

20 Radiance First guess: Bad choice: Solution: L : M S 2 R 4 missing coordinate frame L : (x, ω) [S, F ] 12/37

21 Radiance First guess: Bad choice: Solution: L : M S 2 R 4 missing coordinate frame L : (x, ω) [S, F ] Stokes space S ω : space of all pairs, Stokes vector S and its coordinate frame F L : M S 2 S ω 12/37

22 BSDF BSDF in polarised light transport f : M S 2 S 2? 13/37

23 BSDF First guess: f : M S 2 S 2 R /37

24 BSDF First guess: Bad choice: f : M S 2 S 2 R 4 4 missing coordinate frames 13/37

25 BSDF First guess: Bad choice: Solution: f : M S 2 S 2 R 4 4 missing coordinate frames f : (x, ω i, ω o ) [M, F i, F o ] 13/37

26 BSDF First guess: Bad choice: Solution: f : M S 2 S 2 R 4 4 missing coordinate frames f : (x, ω i, ω o ) [M, F i, F o ] Mueller space M ωo ω i : space of all triplets, Mueller matrix M, incoming frame F i and outgoing frame F o f : M S 2 S 2 M ωo ω i 13/37

27 Operations on S ω and M ω o ω i Define integration and multiplication L o = L e + f(ω i, ω o ) L i (ω i ) dωi S 2 14/37

28 Operations on S ω and M ω o ω i Define integration and multiplication L o = L e + f(ω i, ω o ) L i (ω i ) dωi S 2 Multiplication [M, F i, F o ] [S, F ] = [MF i F }{{ 1 S, F } o ] transformation from F to F i 14/37

29 Operations on S ω and M ω o ω i Define integration and multiplication L o = L e + f(ω i, ω o ) L i (ω i ) dωi S 2 Multiplication Integration addition [M, F i, F o ] [S, F ] = [MF i F }{{ 1 S, F } o ] transformation from F to F i [S, F ]+[T, G] = [S + F } G {{ 1 } T, F ] transformation from G to F 14/37

30 Importance Measurement equation I = W e (ω)l i (ω) dω S 2 Importance camera/eye sensitivity 15/37

31 Measurement S = F } G {{ 1 } S I = 1 ( ) S 1 2 S 2 frame transformation S 3 S 0 16/37

32 Measurement S = F } G {{ 1 } S frame transformation I S I 1 I 2 = S S 2 I S 3 17/37

33 Importance Importance for polarised light transport W T : (x, ω) [W T, F ] 18/37

34 Importance Importance for polarised light transport W T : (x, ω) [W T, F ] Importance space I ωi : space of all pairs, measurement matrix W T and its coordinate frame F W T : M S 2 I ω 18/37

35 Importance Importance for polarised light transport W T : (x, ω) [W T, F ] Importance space I ωi : space of all pairs, measurement matrix W T and its coordinate frame F W T : M S 2 I ω Define multiplication I = We T (ω) L i (ω) dω S 2 18/37

36 Summary of Theory We have defined radiance, BSDF and importance in the context of the polarising light transport Rendering and measurement equations are now well defined Path integral formulation is now well defined too 19/37

37 Reference implementation 20/37

38 Target platform Extending SmallUPBP Non-polarising algorithms already implemented. Better presents the necessary changes. 21/37

39 Polarisation-Capable Uni-Directional Path Tracing 22/37

40 Polarisation-Capable Uni-Directional Path Tracing S ω Light, M ω i ω o Attenuation Light sources and BSDF return them Potential reordering of expressions 22/37

41 Polarisation-Capable Uni-Directional Path Tracing S ω Light, M ω i ω o Attenuation Light sources and BSDF return them Potential reordering of expressions Matches standad polarisation support Data type separation Clear changes to light transport code itself 22/37

42 Polarisation-Capable Bi-Directional Path Tracing Importance Matrix representation of importance Measuring Stokes components identity matrix Coordinate frame based on camera orientation 23/37

43 Polarisation-Capable Bi-Directional Path Tracing Path direction Non-polarising BDPT can disregard path direction with BRDF f(ω i ω o ) = f(ω o ω i ) What about polarising BDPT: f(ω i ω o )? = f(ω o ω i ) 24/37

44 Polarisation-Capable Bi-Directional Path Tracing Path direction Non-polarising BDPT can disregard path direction with BRDF f(ω i ω o ) = f(ω o ω i ) What about polarising BDPT: f(ω i ω o ) f(ω o ω i ) Matrices match, but frames do not. incoming frame must match incoming direction outgoing frame must match outgoing direction Information of path direction propagated 24/37

45 Polarisation-Capable Photon Mapping Tracing works the same Type Light stored in photon map Photons transformed through BSDF into view direction Averaging leads to eligible operations 25/37

46 Polarisation-Capable Volumetric Bi-Directional Path Tracer Equivalent changes to BDPT and VPT Transmittance accumulation + bi-directional = problem Accumulation dependant on path direction 26/37

47 Results and optimizations 27/37

48 Test Scenes diffuse S 0 degree of polarisation overlaid in red 28/37

49 Test Scenes glossy S 0 degree of polarisation overlaid in red 29/37

50 Test Scenes glass S0 M. Mojzı k, T. Skr ivan, A. Wilkie & J. Kr iva nek degree of polarisation overlaid in red Bi-Directional Polarised Light Transport 30/37

51 Test Scenes Volumetric glass S0 M. Mojzı k, T. Skr ivan, A. Wilkie & J. Kr iva nek degree of polarisation overlaid in red Bi-Directional Polarised Light Transport 31/37

52 Bathroom scene S 0 degree of polarisation overlaid in red 32/37

53 Efficiency nonpol naive iterations diffuse glossy glass vol. glass 33/37

54 Efficiency Polarisation support brings overhead Comparing with non-polarising version Optimizations on data types unpolarised Light depolarising Attenuation plain Attenution 34/37

55 Efficiency nonpol naive opti iterations diffuse glossy glass vol. glass 35/37

56 Conclusion Reformulated the radiometry for polarised light Developed reference implmenetation of BDPT, VBDPT and VCM Examined the efficiency of polarisation support and suggested optimizations 36/37

57 Thank you. Acknowledgement Work supported by grants GAR S and SVV /37